White, nominated by President Barack Obama to lead the Securities and Exchange Commission, was retained by the NFL in 2011 to review evidence that team paid players to injure opponents.

The probe resulted in the suspension of several key defensive players and coaches, including Saints head coach Sean Payton. The players suspensions were overturned last year on appeal. The Saints didn’t recover from the suspensions, finishing with a 7-9 win-loss record in 2012, one year after going 13-3. The team won Super Bowl XLIV in 2010.

“If Mary Jo’s work at the SEC is anything close to her botched work for the NFL, folks who want to protect their investments, like the victims of the Stanford Ponzi scheme, are in trouble,” Vitter said in a statement.

The senator’s state is home to many Stanford investors.

The three-member arbitration panel that overturned the players’ suspensions faulted NFL Commissioner Roger Goodell for his handling of the discipline. It didn’t address White’s review of the facts or the quality of the investigation.

Vitter’s staff says he plans to ask White how many of the NFL’s cooperating witnesses actually mentioned a “pay for injury” program, and if any of them had an interest in verifying the league’s claims.